Part 1 - ANOVA

The General Social Survey collects data on demographics, education, and work, among many other characteristics of US residents. Using ANOVA, we can consider educational attainment levels for all 1,172 respondents at once. Below are the distributions of hours worked by educational attainment and relevant summary statistics that will be helpful in carrying out this analysis.

1. (2 points) Write the null and alternative hypotheses for evaluating whether the average number of hours worked varies across the five groups.

2. Using the information provided, assess whether the following conditions necessary to accurately perform an ANOVA F test are met:

a. (0.5 point) Are the observations in the study independent?

b. (0.5 point) Are the sample sizes sufficiently large? (Hint: the n row of the table,above provides the sample sizes of each group.)

c. (0.5 point) is the variation in the groups about equal from one group to the next?

(Hint: use the spread of the boxplots and standard deviation values from the

table to assess this condition.)

3. To assess whether there is a significant difference in the average number of hours worked between one or more of the groups, we need to determine the mean squares between groups (MSG) and the mean squares within groups (MSE). Each of these values has an associated degrees of freedom.

a. (1 point) Determine the degrees of freedom associated with the MSG.

b. (1 point) Determine the degrees of freedom associated with the MSE.

4. (1 point) An ANOVA was performed in R. The estimate for the mean squares between groups is MSG = 501.54 and the resulting F statistic is equal to 2.189. Determine the average variation within each group. That is, calculate the MSE.

5. (2 points) Using the F statistic from question 4 and the two values for the degrees of freedom in question 3, calculate the p-value for this test.

6. (2 points) Using the p-value calculated in question 5, write a conclusion for this ANOVA F test. (Hint: your conclusion should include a statement of evidence in favor of the alternative and a statement as to whether the null hypothesis is rejected or not.)